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Let X1, X2, ..., Xn be a random sample from a distribution with probability density function...

Let X1, X2, ..., Xn be a random sample from a distribution with probability density function f(x; θ) = (θ 4/6)x 3 e −θx if 0 < x < ∞ and 0 otherwise where θ > 0

. a. Justify the claim that Y = X1 + X2 + ... + Xn is a complete sufficient statistic for θ. b. Compute E(1/Y ) and find the function of Y which is the unique minimum variance unbiased estimator of θ.

b.  Compute E(1/Y ) and find the function of Y which is the unique minimum variance unbiased estimator of θ.

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